Low-Rank Hankel Methods for Spectral Signal Processing
From Spectral Compressed Sensing to Blind Super-Resolution and Demixing
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Beschreibung
This book offers a unified introduction to low-rank Hankel methods for modern spectral signal processing, which are widely used in high-resolution radar/sonar imaging, DOA estimation and array processing, massive MIMO channel estimation, medical and astronomical imaging, and integrated sensing and communication systems. It provides a practical pathway from basic Hankel structures to state-of-the-art algorithms for spectral compressed sensing, blind super-resolution, and joint blind super-resolution and demixing. Focusing on spectrally sparse signals, the book shows how to exploit Hankel matrix and tensor structures to recover continuous-domain frequencies from few, noisy, or nonuniform samples. It explains when convex approaches based on nuclear or atomic norms guarantee exact recovery, and why they become computationally prohibitive in large-scale radar, imaging, and communication systems. Building on this foundation, the text introduces fast nonconvex schemes—projected, vanilla, scaled, and Riemannian gradient methods—that leverage low-rank factorization of Hankel (and vectorized Hankel) matrices with rigorous convergence and sample complexity guarantees. A central theme is handling realistic, “blind” scenarios where point spread functions or channels are unknown, and multi-user mixtures must be demixed before super-resolving fine spectral details. The book systematically treats these challenges, from single-measurement spectral compressed sensing to multi-measurement Hankel tensor completion and integrated sensing-and-communication style joint blind super-resolution and demixing. Throughout, theoretical insights are closely linked to algorithm design and numerical behavior, helping readers understand not only how to implement methods, but when and why they work. This volume targets advanced graduate students, researchers, and R&D engineers in signal processing, applied mathematics, radar and wireless communications, and related areas who need reliable and efficient tools for spectral compressed sensing, blind super-resolution, and demixing in high-dimensional applications.
Integrates convex, non-convex, and Riemannian methods into a unified framework for spectral signal recovery Unifies low-rank Hankel modeling techniques with rigorous theory and scalable algorithmic implementations Bridges mathematical theory and practical applications in next-generation sensing and communication systems
Autor*in
Xu Zhang
Themen in »Low-Rank Hankel Methods for Spectral Signal Processing«
Low-rank Hankel methods for signal processing Spectral compressed sensing algorithms Joint blind super-resolution and demixing Spectrally sparse signal reconstruction Hankel-structured signal recovery Spectral signal processing Hankel tensor decomposition Low-rank matrix completion in the Fourier domain Structured low-rank signal estimation Scaled gradient methods for blind deconvolution